364 Oraiidparental Inheritance in Horses 
It would thus appeal" that there is very little difference in the degrees of 
resemblance between grandparents and grandchildren in the cases of the most 
complete data, i.e. those for the horse and man. The dog presents curious 
anomalies, so curious that one must feel grave doubts as to the accuracy of the 
record. Taking the whole series as it stands the mean grandparental correlation 
is about "27. It is doubtful however whether the parthenogenetic grandmothers 
ought not to be treated as " midgrandpareuts." In this case the grandparental 
relation for Daphnia reduces to '1360 and for Aphis to 'ISIS — results more closely 
in accordance with the Basset Hound value than with those for the horse and 
man. What we need in order to throw light on the whole subject is the measure- 
ment of grandparental inheritance for " blending " characters in the case of sexual 
reproduction. At present we have only data for alternative characters for sexual 
reproduction and blending characters for parthenogenetic reproduction, and it is 
by no means certain that the comparison is a fair one. In the case of man it is 
not easy to obtain numerous data for a blending character in grandparents and 
offspring, for such characters are rarely put on record : possibly something might be 
done in the case of measurements of the cephalic index in not too old grandparents 
and young grandchildren. As a rule, however, we cannot obtain directly adult 
characters for both. The breeding of small mammals or insects ad hoc seems the 
best solution of the difficulty. At any rate it is clear that we want further 
observations on grandparental inheritance and if possible on material where the 
influence of environment and the death-rate are not so great as in Daphnia and 
Aphis. From a wide range of series of both blending and alternative characters it 
is now known that the parental correlation is about '45, but until we know the 
grandparental correlation with equal certainty it is impossible really to determine 
the weight to be given to earlier stages of the ancestry. What, however, is clear 
at present is that the values thus far found are inconsistent with Mr Galton's 
original i*, with the "15 deduced by Professor Pearson -f- from his fuller treatment 
of Galton's Law, or even very satisfactorily with the •25 which he sets as a limit in 
his paper on the Law of Re version |. It is to be hoped that biometricians will 
turn their attention to this important point by making direct observations of 
blending characters in grandparents and their sexually produced grandchildren. 
* Natural Inheritance, p. 133. 
t R. S. Proc. Vol. 62, p. 397. 
+ Ibid. Vol. 66, p. 149. 
